Accurate customer demand data is important to print shop design, projection of operational costs for a print shop, determining contract pricing, performing customer account management and/or the like. Demand data from a print shop can be used to simulate and optimize print shop configurations. However, this data collection process can be expensive and time-consuming in many instances.
Bootstrapping is a resampling technique used to study the sampling distribution of an estimator such as, for example, sample mean, sample deviation and/or the like. Bootstrapping typically involves randomly resampling (with replacement) from a sample used as a surrogate population. A sample statistic is computed on each of the bootstrap samples and a sampling distribution is created. For example, given a random sample of size n (X1, X2, X3, . . . , Xn), the corresponding sample statistic calculated from this sample may be represented by {circumflex over (θ)}·{circumflex over (θ)}B may represent a random quantity that represents some statistic calculated from the sample such as, for example, a mean, sum of random variables and/or the like. As the limit n→∞, {circumflex over (θ)}B follows a normal distribution with {circumflex over (θ)} as the center and
  s      n  as the standard deviation, where s is the sample standard deviation computed from (X1, X2, X3, . . . , Xn).
Bootstrapping is commonly used on underlying distributions that are normal or that belong to an exponential family of distributions. However, heavy-tailed distributions behave quite differently than normal distributions. Because their tails decline relatively slowly, the probability of very large observations is not negligible. Heavy-tailed distributions have infinite variance indicating high variability in the underlying process that generates these distributions.